Frustrated total internal reflection (FTIR) happens when light that ought to reflect entirely instead tunnels across a microscopic gap into a third medium. It is the party trick where your fingerprints appear inside a glass of water. It is how optical fingerprint scanners read your thumb. And it is a nuisance that fibre optic cables are carefully designed to avoid. Here is what FTIR is, how the evanescent wave makes it possible, and where it matters.
Picture looking into the top of a glass of water held tightly in your hand. The surface you are looking through is a water-air boundary. If you hold the glass loosely, that boundary reflects like a mirror — you see your own reflection, not your hand. But press harder, and the ridges of your fingerprints appear, ghostly and disembodied, on the inside of the glass. The whorls of your finger have spoiled the total internal reflection where they make contact. That is FTIR in action.
What is total internal reflection?
Before FTIR makes sense, you need total internal reflection (TIR). TIR happens when light travelling through a denser medium (higher refractive index) hits the boundary with a rarer medium (lower refractive index) at an angle greater than the critical angle. The light reflects back entirely — 100% of it — with no transmission into the rarer medium.
Our guide on total internal reflection covers the three conditions in detail with worked examples. The key point for FTIR: during TIR, an evanescent wave extends a short distance into the rarer medium adjacent to the interface. It decays exponentially and normally carries no energy away.
What is an evanescent wave?
The evanescent wave is the clue that something is happening on the other side of the boundary, even though no light is supposed to be transmitting. Think of it like the rumble you feel through the floor when a train passes nearby — you are not on the train, but the vibration reaches you. The evanescent wave is that vibration: a faint, non-propagating field that exists only within about one wavelength of the interface.
In TIR, the evanescent wave penetrates the rarer medium but its amplitude drops off exponentially. Within a few hundred nanometres (roughly one wavelength of visible light), it is essentially zero. Because it decays so fast, it cannot carry energy away from the boundary. The reflection stays total.
What is frustrated total internal reflection?
FTIR occurs when a third medium — one with a higher refractive index than the gap material — is brought within the evanescent field. The evanescent wave now has a path into the third medium before it fully decays. Instead of decaying to nothing, it couples into the third medium and re-establishes a propagating wave. Light tunnels across the gap.
The term "frustrated" comes from the fact that the reflection is no longer total. The TIR has been "frustrated" — spoiled — by the presence of the third medium. The closer the third medium gets, the more light tunnels across.
The RP Photonics encyclopedia entry on frustrated total internal reflection provides a detailed technical explanation with diagrams showing how the evanescent field couples across the gap.
3 conditions for FTIR
FTIR does not happen automatically. Three conditions must be satisfied:
1. TIR must already be taking place. The angle of incidence must exceed the critical angle for the first boundary. If the light is not undergoing TIR in the first place, there is no evanescent wave to frustrate.
2. A third medium with a higher refractive index must be within the evanescent field. The third medium must be close enough — typically within a few wavelengths of the boundary — that the evanescent wave has not fully decayed. For visible light, this means a gap of a few hundred nanometres at most.
3. The gap must be filled with a material of lower refractive index than either the first or third medium. This is usually air (n ≈ 1.00), but it could be water or another low-index material. The gap is what the evanescent wave has to tunnel through.
The exact transmission through the gap depends on four factors: the wavelength of the light, the thickness of the gap, the refractive indices of all three media, and the angle of incidence. The Wikipedia section on FTIR explains how the amplitude of the evanescent wave decays exponentially and why a narrow gap is essential.
Where you see FTIR
Fingerprint scanners
Optical fingerprint scanners were one of the first commercial applications of FTIR. A glass platen (the surface you press your finger against) acts as the first medium. Light inside the platen undergoes TIR at the top surface. Where a fingerprint ridge presses against the glass, the skin (higher refractive index) comes within the evanescent field, coupling light out of the platen and scattering or absorbing it. Where the valleys of the fingerprint do not touch, TIR remains intact.
The result: the valleys appear bright (full reflection) and the ridges appear dark (frustrated reflection). A camera below the platen captures this pattern as the fingerprint image. Modern smartphones have moved to capacitive sensors, but many access control systems and forensic scanners still use FTIR-based optical fingerprint readers.
Fibre optics signal loss
In optical fibres, FTIR is a nuisance. The core of the fibre carries the signal by TIR at the core-cladding boundary. The cladding has a lower refractive index, so TIR keeps the light inside the core. But if an external object with a higher refractive index comes into contact with the fibre — or even close enough to reach the evanescent field — some light can tunnel out. This is why fibre cables have protective jackets and why bending a fibre too sharply can cause leakage: the bend pushes the mode field closer to the boundary.
The critical angle for the boundary (41.8° for crown glass to air) determines how steep the angle of incidence must be for TIR — and therefore how vulnerable the fibre is to FTIR from external contact.
Biological and chemical sensors
FTIR is the operating principle behind evanescent-wave biosensors. A waveguide (usually a glass slide or optical fibre) carries light that undergoes TIR at the surface. When biomolecules bind to the surface within the evanescent field, they change the local refractive index or absorb the evanescent wave, frustrating the TIR. The change in transmitted or reflected light reveals the presence and concentration of the target molecule.
This technique is used in medical diagnostics, environmental monitoring, and food safety testing because it does not require labelling the target molecules with fluorescent tags.
Optical touch screens
Some large-format interactive displays use FTIR for multitouch sensing. Infrared LEDs shine light into a glass or acrylic panel, where it undergoes TIR. When a finger touches the surface, it frustrates the TIR at the contact point, scattering infrared light downward. Cameras or sensors below the panel detect the scattered light and calculate the touch position.
The RP Photonics encyclopedia also discusses how FTIR is used for input and output coupling in optical resonators, where a prism is brought progressively closer to a reflection point to extract light from the resonator.
FTIR vs attenuated total reflectance (ATR)
Do not confuse FTIR with ATR (attenuated total reflectance). The two phenomena sound similar but the mechanism is different:
- FTIR: light tunnels across a gap into a third medium. The reflection is reduced because energy is transmitted, not absorbed.
- ATR: the external medium absorbs energy from the evanescent wave. The reflection is reduced because energy is absorbed in the rarer medium itself. ATR spectroscopy is a standard analytical chemistry technique.
The common thread: both involve the evanescent wave. The difference: FTIR is about transmission into a third medium; ATR is about absorption in the second medium.
Common misconception: FTIR only happens with direct contact
A common assumption is that the third medium must physically touch the first medium for FTIR to occur. Direct contact is not required. The third medium only needs to be within the evanescent field — typically less than a wavelength away. This is why you need to squeeze the glass of water tightly for the fingerprints to appear: the pressure reduces the air gap between your skin and the glass into the evanescent range.
The exponential decay of the evanescent wave means that the amount of transmitted light drops off extremely fast with distance. The Ansys Optics guide on modeling FTIR shows how a 100-nanometre air gap transmits about 80% of the light, while a slightly larger gap drops transmission to nearly zero.
For a deeper look at how the critical angle connects TIR and FTIR, see our guide on the critical angle formula. The physics of why light reflects instead of refracting at surfaces is covered in reflection of light examples.
Frequently Asked Questions
What is frustrated total internal reflection?
Frustrated total internal reflection (FTIR) occurs when a third medium is brought extremely close to the boundary where total internal reflection is taking place. The evanescent wave that normally decays in the gap instead reaches the third medium and allows light to tunnel across, reducing the reflection below 100 percent.
What is the difference between total internal reflection and frustrated total internal reflection?
In total internal reflection, all light reflects back into the denser medium. In frustrated total internal reflection, some light tunnels across a narrow gap into a third medium because the evanescent wave has not yet fully decayed. The reflection is no longer total — it is 'frustrated.'
What is an evanescent wave?
An evanescent wave is an optical field that extends a short distance into the rarer medium during total internal reflection. Its amplitude decays exponentially with distance and normally carries no energy away from the interface. FTIR occurs when a third medium intercepts this field before it decays.
How does a fingerprint scanner use FTIR?
Optical fingerprint scanners use frustrated total internal reflection. Light inside a glass platen undergoes TIR everywhere. Where a fingerprint ridge touches the glass, the skin's higher refractive index couples the evanescent wave across the gap, absorbing or scattering the light. The valleys do not touch, so TIR remains intact. The resulting pattern of bright and dark spots maps the fingerprint.
Is FTIR the same as attenuated total reflectance?
No. ATR (attenuated total reflectance) occurs when the external medium absorbs energy from the evanescent wave, reducing reflection. FTIR occurs when a third medium provides a path for light to tunnel across the gap. ATR is about absorption; FTIR is about transmission into a third medium.
Can FTIR happen in optical fibres?
Yes, but it is usually undesirable. In a fibre optic cable, FTIR can cause signal loss if an external object with a higher refractive index comes too close to the core, allowing some light to tunnel out of the waveguide. This is why fibre cladding is essential to keep the evanescent field contained.
About Umar Farooq
Umar Farooq writes in-depth guides on the physics of light and optics — from reflection, refraction, and lenses to diffraction, lasers, and fiber optics, explained from first principles.
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